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On annihilators in BL-algebras

Yu Xi Zou, Xiao Long Xin, Peng Fei He (2016)

Open Mathematics

In the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice (I(L), ⊆) is pseudo-complemented, and for any ideal I, its pseudo-complement is the annihilator I⊥ of I. Also, we define the An (L) to be the set of all annihilators of L, then we have that (An(L); ⋂,∧An(L),⊥,0, L) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study some properties...

On asymptotic behaviour of universal fuzzy measures

Ladislav Mišík, János T. Tóth (2006)

Kybernetika

The asymptotic behaviour of universal fuzzy measures is investigated in the present paper. For each universal fuzzy measure a class of fuzzy measures preserving some natural properties is defined by means of convergence with respect to ultrafilters.

On automorphisms of Boolean algebras embedded in P (ω)/fin

Magdalena Grzech (1996)

Fundamenta Mathematicae

We prove that, under CH, for each Boolean algebra A of cardinality at most the continuum there is an embedding of A into P(ω)/fin such that each automorphism of A can be extended to an automorphism of P(ω)/fin. We also describe a model of ZFC + MA(σ-linked) in which the continuum is arbitrarily large and the above assertion holds true.

On automorphisms of the Banach space / c

Piotr Koszmider, Cristóbal Rodríguez-Porras (2016)

Fundamenta Mathematicae

We investigate Banach space automorphisms T : / c / c focusing on the possibility of representing their fragments of the form T B , A : ( A ) / c ( A ) ( B ) / c ( B ) for A,B ⊆ ℕ infinite by means of linear operators from ( A ) into ( B ) , infinite A×B-matrices, continuous maps from B* = βB∖B into A*, or bijections from B to A. This leads to the analysis of general bounded linear operators on / c . We present many examples, introduce and investigate several classes of operators, for some of them we obtain satisfactory representations and for others give...

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